Mine is pretty simple. The combination of two nicknames I had in my life.
Bam in high school (loosely based on my initials).
And speedy later in life when I had the handle 'Speed Racer' on the CB radio. I picked Speed Racer because at around the time I got onto the CB I was always getting pulled over by the cops for speeding. Luckily, everytime I got pulled over it was by a different cop, or law enforcement agency, so I kept getting verbal or written warnings, or just a $10 seatbelt ticket. Got 22 warnings before I finally got my first real ticket that took a big chunk of money out of my pocket. Got 3 or 4 tickets before I finally matured and slowed down, and I haven't gotten a speeding ticket in the last 5 years or so. There was a group of 4 State Patrol officers who would come into the place where I worked and have coffee. One day, they all realized that each one of them had pulled me over at one time or another, so they got a chuckle out of that and called me 'speedy'.
And around that time there was the ESPN commercials for Nascar where they used the cartoon character 'speed racer'. So one of my friends said "they should start calling you speed racer" and then he chanted the "go, go speed racer, go, go" phrase from those commercials. Most people just started calling me Speedy instead of Speed Racer, so that nickname sort of stuck. (I still know people who I see all the time and they don't know my real name, they just know me as Speedy).
So then I got a computer and internet access, and I didn't realize that I needed an account name right then, so I only had a few minutes to think of a name. Bam, Speedy, and SpeedRacer were already taken, so I just combined the two to Bamspeedy. So then when going to chatrooms and stuff I just used the same name.